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Explanation: A monomial is a polynomial with only one term, and its degree is determined by the exponent of that term. Therefore, the degree of a monomial is equal to the exponent of its variable, which is at least 1 if it is not a constant.
Explanation: The zero polynomial is unique in that it does not have a defined degree because it does not have any non-zero terms. This makes it different from other polynomials, which have degrees based on their highest power of the variable.
Explanation: The Factor Theorem states that if a polynomial p evaluated at a certain value a equals zero, then (x - a) is a factor of that polynomial. This is a fundamental concept in polynomial factorization.
Explanation: A binomial is defined as a polynomial that contains exactly two terms. The polynomial x + 1 fits this definition as it consists of the terms x and 1.
Explanation: The degree of a polynomial is determined by the highest power of the variable present in the polynomial. In this case, the highest power is 3 from the term 5x^3, making the degree of the polynomial 3.
Explanation: A polynomial in one variable must have terms with non-negative integer exponents. The expression 4x^2 - 3x + 7 meets this criterion, while the others do not.
Explanation: A zero polynomial is defined as a polynomial where all coefficients are zero, resulting in the expression being equal to zero for all values of the variable.
Explanation: A quadratic polynomial is defined as a polynomial of degree two, which can be expressed in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
Explanation: The Factor Theorem states that if p(a) = 0 for a polynomial p(x), then (x - a) is a factor of p(x). This theorem is essential for factorizing polynomials.
Explanation: A cubic polynomial is defined as a polynomial of degree three. The expression x^3 - 3x^2 + 2x - 1 has a highest degree of 3, making it cubic.
Explanation: The degree of a polynomial is determined by the highest exponent of its variable. In this case, the highest exponent is 2 from the term -y^2.
Explanation: A binomial is an algebraic expression containing two terms. The expression x^35 - 1 has two terms and the highest degree is 35, making it a binomial of degree 35.
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